## Kinematics of a fastball

Let's analyze the motion of a fastball. First, consider the motion of the ball as it travels from the pitcher's hand to home plate.

Suppose the pitcher throws a ball which ends up at the level of the top of the batter's helmet, 6.5 feet above the ground, way too high to be a strike.

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Q:  What is the displacement of the ball from
the start to the end of the pitch?

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The ball takes 0.41 seconds to travel from the pitcher's hand to the air above home plate.

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Q:  What is the average velocity of the ball from
the start to the end of the pitch?

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Now, let's look at the motion of the ball while it sits in the pitcher's hand. As he moves through his windup, the ball travels forward in his grasp. Even though the actual motion is pretty complex, we can focus on two points: when the ball is behind him, and just as he releases the ball in front of him:

Here's a short video clip of Boston Red Sox pitcher Clay Buchholz throwing a pitch on April 14, 2013. Each frame is about 1/30 of a second.

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Q:  How many frames does it take for the
ball to move from "behind the pitcher"
to "released in front of the pitcher"?

Q:  What is the average acceleration of the
ball during that brief period?

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